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Journal Articles Semigroup Forum Year : 2023

On the structure of semigroups whose regular elements are completely regular

Abstract

We study the structure of strongly 2-chained semigroups, which can be defined alternatively as semigroups whose regular elements are completely regular. The main result is a semilattice decomposition of these semigroups in terms of ideal extensions of completely simple semigroups by poor semigroups and idempotent-free semigroups.
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hal-04291707 , version 1 (17-11-2023)

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Xavier Mary. On the structure of semigroups whose regular elements are completely regular. Semigroup Forum, 2023, ⟨10.1007/s00233-023-10394-7⟩. ⟨hal-04291707⟩
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